Clopper-Pearson Confidence Interval for Failures Which are Tackled by Countermeasures

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Description

Provides the extended Clopper-Pearson confidence limits for a failure model, where countermeasures are introduced.

Usage

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cm.clopper.pearson.ci(n, size, cm.effect, alpha = 0.1, CI = "upper", uniroot.lower = 0, 
 uniroot.upper = 1, uniroot.maxiter = 1e+05, uniroot.tol = 1e-10)

Arguments

n

sample size.

size

vector of the number of failures for each type.

cm.effect

vector of the success probabilities to solve a failure for each type. Corresponds to the probabilities pi of a generalized binomial distribution.

alpha

significance level for the (1-alpha)* 100% confidence level (default alpha=0.1).

CI

indicates the kind of the confidence interval, options: "upper" (default), "lower", "two.sided".

uniroot.lower

The value of the lower parameter sent to uniroot. Lower bound of the interval to be searched. See uniroot for more details.

uniroot.upper

The value of the upper parameter sent to uniroot. Upper bound of the interval to be searched. See uniroot for more details.

uniroot.maxiter

The value of the maxiter parameter sent to uniroot. Maximum number of iterations. See uniroot for more details.

uniroot.tol

The value of the tol parameter sent to uniroot. Convergence tolerance. See uniroot for more details.

Details

This is an extension of the Clopper-Pearson confidence interval, where different outcome scenarios of the random sampling are weighted by generalized binomial probabilities. The weights are the probabilities for observing 0,...,k failures after the introduction of countermeasures. Computes the confidence limits for the p of a binomial distribution, where p is the failure probability. The failures are tackled by countermeasures for specific failure types with different effectivity. See the references for further information.

Value

A data frame containing the kind of the confidence interval, upper and lower limits and the used significance level alpha.

References

D.Kurz, H.Lewitschnig, J.Pilz, Decision-Theoretical Model for Failures which are Tackled by Countermeasures, IEEE Transactions on Reliability, Vol. 63, No. 2, June 2014.

See Also

uniroot, dgbinom, clopper.pearson.ci

Examples

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## n=110000 tested devices, 2 failures divided in 2 failure types k1=1, k2=1.
## 2 countermeasures with effectivities p1=0.5, p2=0.8
cm.clopper.pearson.ci(110000,size=c(1,1),cm.effect=c(0.5,0.8))
# Confidence.Interval = upper
# Lower.limit = 0
# Upper.limit = 3.32087e-05
# alpha = 0.1